The zero-error side information problem and chromatic numbers (Corresp.)

Abstract-Consider an arbitrarily connected broadcast network of N nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and broadcasts messages to its neighbors. For the case where nodes must transmit an integer number of packets, this paper provides necessary and sufficient conditions which characterize the set of all transmission schemes that permit universal recovery (in which every node learns all k packets). By relaxing the integer transmission constraint, this paper gives a computable lowerbound on the amount of information required to be broadcast to achieve universal recovery. Furthermore, a network-coding-based scheme (computable in polynomial time) can always achieve this lower bound if packet splitting is permitted. In this way, packet splitting can provide a significant reduction in the amount of communication required for universal recovery. For cliques with N nodes, this paper shows that splitting the packet into N − 1 chunks allows the lower bound to be achieved with high probability.

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“…First, consider the following set of inequalites which are a subset of the inequalities described by (5):…”

Section: Proof Of Theoremmentioning

confidence: 99%

Optimal exchange of packets for universal recovery in broadcast networks

Courtade

Xie

Wesel

2010

2010 - Milcom 2010 Military Communications Conference

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“…They showed that this problem is different in nature from the well-known source coding problems previously studied by Witsenhausen in [12]. Their main contribution is an upper bound on ℓ(G), the optimal length of an index code (Definition 2).…”

Section: Definition 1 (Index Code)mentioning

confidence: 96%

Nonlinear Index Coding Outperforming the Linear Optimum

Lubetzky

Stav

2009

IEEE Trans. Inform. Theory

129

103

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The following source coding problem was introduced by Birk and Kol: a sender holds a word x ∈ {0, 1} n , and wishes to broadcast a codeword to n receivers, R 1 , . . . , R n . The receiver R i is interested in x i , and has prior side information comprising some subset of the n bits. This corresponds to a directed graph G on n vertices, where ij is an edge iff R i knows the bit x j . An index code for G is an encoding scheme which enables each R i to always reconstruct x i , given his side information. The minimal word length of an index code was studied by Bar-Yossef, Birk, Jayram and Kol [4]. They introduced a graph parameter, minrk 2 (G), which completely characterizes the length of an optimal linear index code for G. The authors of [4] showed that in various cases linear codes attain the optimal word length, and conjectured that linear index coding is in fact always optimal.In this work, we disprove the main conjecture of [4] in the following strong sense: for any ε > 0 and sufficiently large n, there is an n-vertex graph G so that every linear index code for G requires codewords of length at least n 1−ε , and yet a non-linear index code for G has a word length of n ε . This is achieved by an explicit construction, which extends Alon's variant of the celebrated Ramsey construction of Frankl and Wilson.In addition, we study optimal index codes in various, less restricted, natural models, and prove several related properties of the graph parameter minrk(G).

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“…We note here the interesting discussion between decentralized computation and communication provided by Orlitsky and Roche (2001), as well as by Witsenhausen (1976) where a probability-free construction is considered and a zero-error (non-asymptotic and error-free) computation is considered in the same spirit as in Yao (1979).…”

Section: Connections With Information Theorymentioning

confidence: 99%

Information and Communication Complexity of Networked Control Systems

Yüksel¹

2015

Encyclopedia of Systems and Control

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Information and communication complexity of a networked control system identifies the minimum amount of information exchange needed between the decision makers (such as encoders, controllers and actuators) to achieve a certain objective, which may be in terms of reaching a target state or achieving a given cost threshold. This formulation does not impose any constraints on the computational requirements to perform the communication or control. Both stochastic and deterministic formulations are considered.

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The zero-error side information problem and chromatic numbers (Corresp.)

Cited by 206 publications

References 1 publication

Optimal exchange of packets for universal recovery in broadcast networks

Optimal exchange of packets for universal recovery in broadcast networks

Nonlinear Index Coding Outperforming the Linear Optimum

Information and Communication Complexity of Networked Control Systems

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